Scientific Fuzzy Machine Learning

The prosperity of physics-informed neural networks (PINNS) in solving partial differential equations (PDEs) is steadily improving due to their effective interactions with the physics behind different PDEs. While previous investigations in PINNS have mainly tackled improving loss functions during the training process, the use of different optimization schemes for solving PDEs has been overlooked. This study introduces a novel physics-informed optimization method using an adaptive neural-fuzzy inference system (ANFIS) that integrates reasoning and learning. The pattern Search algorithm is exploited to propagate solutions properly from initial- boundary points to the interior collocation points and balance the interplay between losses derived from these points. In particular, PDE parameters are first mapped into fuzzy membership functions (MFs). Then Pattern Search method steers the ANFIS model to converge properly by tuning the MFs. The proposed method improved convergence speed and prevented the algorithm from getting stuck in poor local minima. Comprehensive experimental results for different partial differential equations confirm the effectiveness of the proposed method. To our knowledge, this is the first time that a PDE has been tackled by employing the scientific fuzzy machine learning.